Problem 7.30 Part A A 1.44-kg block is held in place against the spring by a 33-

Question

Problem 7.30 Part A A 1.44-kg block is held in place against the spring by a 33-N horizontal external force (see the figure). The external force is removed, and the black is projected with a velocity v1 12 ms upon separation from the spring The block descends a ramp and has a velocity v2 2.1 m/s at the bottom. The track is frictionless between points A and B. The block enters a rough section at B, extending to E. The coefficient of kinetic fricdion over this section is 0.31. The velocity of the block is v 3 1.4 m/s at C. The block moves on to D, where it stops. The initial compression of the spring is closest to v O 7.6 cm O 6.3 cm. O 8.8 cm O 3.8 cm. 05.0 cm. Submit My Answers Give Up oblemiD-471004948 hmentPr masteringphysics.com/myct/itemView?assignmentProblemID-47100494&e; https://session.masteringphysics.com/myct/itemView?assign

Explanation / Answer

let x is the compresiion of the spring,

Apply Hook's law

F = k*x

33 = K*x ---(1)

Apply Energy conservation

0.5*m*v1^2 = 0.5*k*x^2

0.5*m*v1^2 = 0.5*(k*x)^2/k

m*v1^2 = (k*x)^2/k

k = (k*x)^2/(m*v1^2)

= (33)^2/(1.44*1.2^2)

= 525.2 N/m

now from equation 1

x = F/k

= 33/525.2

= 0.063 m

= 6.3 cm

so, option 2 is the correct answer.

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